US President Donald Trump hailed the Korea summit as historic but cautioned that "only time will tell".
Pyongyang and Seoul agreed in a joint statement on Friday that they have agreed to rid their peninsula of nuclear weapons.
North and South Korea will also pursue a peace treaty with the United States and China to formally end the 1950-1953 Korean War.
The US president tweeted:
The summit was the highest-level encounter yet in a whirlwind of nuclear diplomacy, and was intended to pave the way for the much-anticipated encounter between Kim Jong-un and Mr Trump.
Last year, Pyongyang carried out its sixth nuclear test, by far its most powerful to date, and launched missiles capable of reaching the US mainland.
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Korea summit
North and South agree to seek peace and complete denuclearisation
Pictures: Korea's historic summit
South Koreans captivated by 'cute' Kim
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Its actions sent tensions soaring as Mr Kim and Mr Trump traded personal insults and threats of war.
Elsewhere, the North's sole major ally, China, welcomed the summit saying it applauds the countries' leaders for taking a "historic step" toward peace.
Foreign Ministry spokeswoman Hua Chunying said Beijing wishes that the meeting between Mr Kim South Korean President Moon Jae-in will achieve a "positive result".
Ms Hua quoted the Chinese writer Lu Xun: "After all of the suffering, the brotherly friendship still exists; with a smile, let's forget about the debt of gratitude and revenge."
She said China looked forward to taking this summit as an opportunity to expand into a "new journey of long-term peace and stability on the peninsula".
Japanese Prime Minister Shinzo Abe welcomed a summit between the two Koreas, urging Pyongyang to take "concrete action".
"Today President Moon Jae-in and Chairman Kim Jong-un held earnest discussions about North Korea's denuclearisation. I want to welcome that as a positive move toward comprehensive resolution of various issues concerning North Korea," Mr Abe said in Tokyo.
"We strongly hope that North Korea will take concrete action through this meeting and a summit between the US and North Korea."
Earlier, Australian Prime Minister Malcolm Turnbull and Foreign Minister Julie Bishop said they "cautiously welcome" the summit.
German Foreign Minister Heiko Maas said North Korea's announcement that it would immediately suspend nuclear and missile tests was a step in the right direction but added that Pyongyang must reveal its nuclear and missile programme.
"To enter into a serious political process working towards the complete denuclearisation of North Korea, it is however necessary for Pyongyang to follow specific steps and to disclose its complete nuclear and missile programme in a verifiable way," Mr Maas said on Saturday.
Federica Mogherini, the High Representative of the EU for Foreign Affairs and Security Policy, said the announcement was "a positive, long sought-after step on the path that has now to lead to the country's complete, verifiable and irreversible denuclearisation."
It was also a move towards "the full respect for its international obligations and all relevant UN Security Council resolutions."
Boris Johnson, the British Foreign Secretary also embraced the prospect of dismantling the nuclear programme.
“I welcome the announcement that the two Koreas will work towards the complete, verifiable, and irreversible denuclearisation of North Korea, improve bilateral ties and reduce border tensions," he said. “This historic summit is not the end in itself. There are still many questions to be answered. Kim Jong-un’s commitment to halt all nuclear and intercontinental and intermediate range ballistic missiles tests is a positive step. We hope this indicates an intention to negotiate in good faith and that Kim has heeded the clear message to North Korea that only a change of course can bring the security and prosperity it claims to seek.
“The UK will continue to work with our international partners to strictly enforce existing sanctions until such time that North Korea turns its commitments into concrete steps towards denuclearisation.”